Towards a reproducible snow load map – an example for Austria

Abstract. The European Committee for Standardization defines zonings and calculation criteria for different European regions to assign snow loads for structural design. In the Alpine region these defaults are quite coarse; countries therefore use their own products, and inconsistencies at national borders are a common problem. A new methodology to derive a snow load map for Austria is presented, which is reproducible and could be used across borders. It is based on (i) modeling snow loads with the specially developed Δsnow model at 897 sophistically quality controlled snow depth series in Austria and neighboring countries and (ii) a generalized additive model where covariates and their combinations are represented by penalized regression splines, fitted to series of yearly snow load maxima derived in the first step. This results in spatially modeled snow load extremes. The new approach outperforms a standard smooth model and is much more accurate than the currently used Austrian snow load map when compared to the RMSE of the 50-year snow load return values through a cross-validation procedure. No zoning is necessary, and the new map's RMSE of station-wise estimated 50-year generalized extreme value (GEV) return levels gradually rises to 2.2 kN m−2 at an elevation of 2000 m. The bias is 0.18 kN m−2 and positive across all elevations. When restricting the range of validity of the new map to 2000 m elevation, negative bias values that significantly underestimate 50-year snow loads at a very small number of stations are the only objective problem that has to be solved before the new map can be proposed as a successor of the current Austrian snow load map.

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Towards a reproducible snow load map – an example for Austria

10.5194/egusphere-egu21-8859 ◽

2021 ◽

Author(s):

Harald Schellander ◽

Michael Winkler ◽

Tobias Hell

Keyword(s):

Additive Model ◽

Penalized Regression ◽

Extreme Value ◽

Ease Of Use ◽

Return Level ◽

Snow Load ◽

Snow Model ◽

Penalized Regression Splines ◽

Extreme Value Model ◽

Value Model

The European Committee for Standardization provides coarse rules for the estimation of snow load maps for structural design. European countries can&#160;apply their own methodologies, resulting in inconsistencies for the 50-year return level of snow load at national borders. Commonly used approaches base on more or less sophisticated interpolation of snow depths with a subsequent assignment of snow density, or spatial extreme value interpolation of snow load measurements. &#160;We propose a novel methodology for Austria, where snow load observations are not available. It is based on (1) modeling yearly snow load maxima with the specially developed &#8710;SNOW model, and (2) a generalized additive model, where explaining covariates and their combinations are represented by penalized regression splines, fitted to such derived snow load series. Results show an RMSE of 0.7 kN/m2, and a BIAS of -0.2 kN/m2 over all altitudes, thereby outperforming a smooth spatial extreme value model and the actual Austrian standard, when compared to locally estimated, &#8220;quasi-observed &#8220; 50-year snow load maxima at 870 stations in and tightly around Austria.The new approach requires no zoning and provides a reproducible and transparent approach. Due to the relatively ease of use and snow depth measurements as single prerequisite, the method is applicable in other countries as well. Negative BIASes, that significantly underestimate 50-year snow loads at a small number of stations, are the only objective problem that has to be solved before the new map can be proposed as a successor of the actual Austrian snow load map.

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GAMs with integrated model selection using penalized regression splines and applications to environmental modelling

Ecological Modelling ◽

10.1016/s0304-3800(02)00193-x ◽

2002 ◽

Vol 157 (2-3) ◽

pp. 157-177 ◽

Cited By ~ 455

Author(s):

Simon N. Wood ◽

Nicole H. Augustin

Keyword(s):

Model Selection ◽

Penalized Regression ◽

Integrated Model ◽

Regression Splines ◽

Environmental Modelling ◽

Penalized Regression Splines

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Estimating the impact of vaccination using age–time-dependent incidence rates of hepatitis B

Epidemiology and Infection ◽

10.1017/s0950268807008692 ◽

2007 ◽

Vol 136 (3) ◽

pp. 341-351 ◽

Cited By ~ 9

Author(s):

N. HENS ◽

M. AERTS ◽

Z. SHKEDY ◽

P. KUNG'U KIMANI ◽

M. KOJOUHOROVA ◽

...

Keyword(s):

Hepatitis B ◽

Generalized Additive Models ◽

Additive Model ◽

Penalized Regression ◽

Incidence Rates ◽

Additive Models ◽

Time Dependent ◽

Model Framework ◽

Penalized Regression Splines ◽

The Impact

SUMMARYThe objective of this study was to model the age–time-dependent incidence of hepatitis B while estimating the impact of vaccination. While stochastic models/time-series have been used before to model hepatitis B cases in the absence of knowledge on the number of susceptibles, this paper proposed using a method that fits into the generalized additive model framework. Generalized additive models with penalized regression splines are used to exploit the underlying continuity of both age and time in a flexible non-parametric way. Based on a unique case notification dataset, we have shown that the implemented immunization programme in Bulgaria resulted in a significant decrease in incidence for infants in their first year of life with 82% (79–84%). Moreover, we have shown that conditional on an assumed baseline susceptibility percentage, a smooth force-of-infection profile can be obtained from which two local maxima were observed at ages 9 and 24 years.

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Climate sensitivity and resistance under pure- and mixed-stand scenarios in Lower Austria evaluated with distributed lag models and penalized regression splines for tree-ring time series

European Journal of Forest Research ◽

10.1007/s10342-019-01234-x ◽

2019 ◽

Vol 139 (2) ◽

pp. 189-211 ◽

Cited By ~ 2

Author(s):

Arne Nothdurft ◽

Markus Engel

Keyword(s):

Tree Ring ◽

Climate Sensitivity ◽

European Beech ◽

Penalized Regression ◽

Mixed Stand ◽

Regression Splines ◽

Mixed Stands ◽

Distributed Lag ◽

Distributed Lag Models ◽

Penalized Regression Splines

Abstract Penalized regression splines and distributed lag models were used to evaluate the effects of species mixing on productivity and climate-related resistance via tree-ring width measurements from sample cores. Data were collected in Lower Austria from sample plots arranged in a triplet design. Triplets were established for sessile oak [Quercus petraea (Matt.) Liebl.] and Scots pine (Pinus sylvestris L.), European beech (Fagus sylvatica L.) and Norway spruce [Picea abies (L.) H. Karst.], and European beech and European larch (Larix decidua Mill.). Mixing shortened the temporal range of time-lagged climate effects for beech, spruce, and larch, but only slightly changed the effects for oak and pine. Beech and spruce as well as beech and larch exhibited contrasting climate responses, which were consequently reversed by mixing. Single-tree productivity was reduced by between − 15% and − 28% in both the mixed oak–pine and beech–spruce stands but only slightly reduced in the mixed beech–larch stands. Measures of climate sensitivity and resistance were derived by model predictions of conditional expectations for simulated climate sequences. The relative climate sensitivity was, respectively, reduced by between − 16 and − 39 percentage points in both the beech–spruce and beech–larch mixed stands. The relative climate sensitivity of pine increased through mixing, but remained unaffected for oak. Mixing increased the resistance in both the beech–larch and the beech–spruce mixed stand. In the mixed oak–pine stand, resistance of pine was decreased and remained unchanged for oak.

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S-Estimation for Penalized Regression Splines

Journal of Computational and Graphical Statistics ◽

10.1198/jcgs.2010.08149 ◽

2010 ◽

Vol 19 (3) ◽

pp. 609-625 ◽

Cited By ~ 14

Author(s):

Kukatharmini Tharmaratnam ◽

Gerda Claeskens ◽

Christophe Croux ◽

Matias Salibián-Barrera

Keyword(s):

Penalized Regression ◽

Regression Splines ◽

Penalized Regression Splines

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Extreme snow loads in Austria

10.5194/egusphere-egu21-3331 ◽

2021 ◽

Author(s):

Michael Winkler ◽

Harald Schellander

Keyword(s):

Structural Design ◽

Snow Depth ◽

Generalized Additive Models ◽

Value Theory ◽

Additive Models ◽

Snow Load ◽

Snow Loads ◽

Snow Model ◽

European Standards ◽

Smooth Map

In the framework of European standards for structural design, acceptable snow loads on constructions and buildings are based on maps for sk, the &#8220;characteristic snow load on the ground&#8221; with an average reoccurrence time of 50 years. The Austrian snow load standard is built on a very detailed zoning map from 2006, but underlying snow data is from the 1980s.An updated snow load map for Austria is presented. It is based on 870 snow depth records with at least 30 years of regular daily observations between 1960 and 2019. &#916;SNOW, a novel snow model, was used to simulate respective snow loads. Extreme value theory and generalized additive models led to a smooth map of extreme snow loads at 50x50m resolution. The methods are transparently published, reproducible and, thus, applicable in other regions as well.The map can reasonably assign sk values up to 2000m altitude, a significant advantage compared to actual standards which are only valid up to 1500m. New insights in the spatial picture of extreme snow loads are provided and the quadratic altitude-sk-relation, which is widely used in snow load standards, is evaluated. Validation with station data reveals a higher accuracy for the presented map than for the currently used snow load map. The number of outliers, i.d. stations with significantly higher or lower sk values than the snow load maps would suggest, could be decreased in comparison with the actual standard. However, some problematic places remain, mostly in topographically and climatologically highly complex areas. In case the presented map will become a new base for future Austrian standards, those places will have to be treated in a special way.

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